I think I'd have been completely thrown when this girl who everyone is pretending is a boy asked to enter the girl-only competition.
Some things that might have gone through my head:
"We're supposed to pretend she's a boy. Will I be accused of transphobia if I say she can enter?"
"If I say she can't enter because she's a boy, will I be accused of transphobia?"
"If I say yes, will some of the boys ask why they can't enter, because she's apparently a boy just like them?"
"If I say no because she's a boy, will some of the boys start saying they're girls so that they can enter?"
"Has she now changed her mind and decided she's a girl after all?"
All this would have happened in the few seconds between her saying she wanted to enter and me having to decide whether to add her name (which name?) to the list.
I think I'd end up thinking "fuck it, I'm doomed" and making a quick decision, aware that no matter what I did it would probably be wrong in some way.